The contingent vote is an electoral system used to elect a single winner, in which the voter ranks the candidates in order of preference. In an election, if no candidate receives an absolute majority of first preference votes, then all but the two leading candidates are eliminated and there is a second count. In the second count the votes of those who supported eliminated candidates are distributed among the two remaining candidates, so that one candidate achieves an absolute majority. The contingent vote is similar to the alternative vote but differs from it in that the alternative vote typically allows for many rounds of counting, whereas under the contingent vote there are never more than two. In the United States both the contingent vote and the alternative vote are often referred to as variants of instant-runoff voting. The contingent vote can also be considered a compressed form of the two round system (runoff system), in which both 'rounds' occur without the need for voters to go to the polls twice.

Today a special variant of the contingent vote is used to elect the President of Sri Lanka. Another variant, called the supplementary vote, is used to elect mayors and Police and Crime Commissioners in England. In the past the ordinary form of the contingent vote was used to elect the Legislative Assembly of Queensland from 1892 to 1942. To date, this has been the longest continuous use of the system anywhere in the world. It was also used in the U.S. state of Alabama in the 1920s.

In an election held using the contingent vote the voters rank the list of candidates in order of preference. Under the most common ballot layout, they place a '1' beside their most preferred candidate, a '2' beside their second most preferred, and so on. In this respect the contingent vote is the same as instant-runoff voting.

There are then a maximum of two rounds of counting. In the first round only first preferences are counted. If a candidate has received an absolute majority of first preferences (i.e. more than half) then he is immediately declared the winner. However, if no candidate has an absolute majority then all but the two candidates with the most first preferences are eliminated, and there is a second round. In the second round the votes of the voters whose first preference had been eliminated are transferred to whichever of the two remaining candidates were ranked the highest. The votes are then counted and whichever candidate has an absolute majority is declared elected.

Imagine an election in which there are three candidates: Andrew, Brian and Catherine. There are 100 voters and they vote as follows (third preferences are omitted):

#

30 voters

6 voters

9 voters

7 voters

28 voters

20 voters

1st

Andrew

Andrew

Brian

Brian

Catherine

Catherine

2nd

Brian

Catherine

Andrew

Catherine

Brian

Andrew

1. To begin the count first preferences are counted, and the tallies stand at:

Andrew: 36

Brian: 16

Catherine: 48

2. No candidate has an absolute majority of votes (this would be 51), so the two candidates with most votes proceed to a second round and Brian, who has the fewest votes, is excluded. 9 of Brian's supporters have given Andrew as their second preference, and 7 have given Catherine as their second preference, so these votes transfer to Andrew and Catherine respectively. The tallies then become:

Imagine another election in which there are four candidates: Andrea, Brad, Carter and Delilah. There are 120 voters and they vote as follows (fourth preferences are omitted):

#

34 voters

17 voters

22 voters

10 voters

37 voters

1st

Andrea

Brad

Carter

Carter

Delilah

2nd

Brad

Carter

Brad

Delilah

Carter

3rd

Carter

Andrea

Andrea

Brad

Brad

The count would proceed as follows:

Andrea

Brad

Carter

Delilah

Round 1

34

17

32

37

Round 2

73

17 0

32 0

47

Round 1: First preferences are tallied and no candidate has a majority (in this election an absolute majority would be 61).

Round 2: Andrea and Delilah have the most votes so they proceed to a second round while Brad and Carter are excluded. The votes of Brad and Carter supporters are now distributed among the two survivors. To do this the ballot papers of Brad and Carter supporters are examined to see which of the two remaining candidates each voter has ranked higher. The preferences expressed on the ballot papers of Brad and Carter supporters were as follows:

#

17 voters

22 voters

10 voters

1st

Brad

Carter

Carter

2nd

Carter

Brad

Delilah

3rd

Andrea

Andrea

Brad

4th

Delilah

Delilah

Andrea

On the basis of these ballot papers 39 votes are transferred to Andrea and 10 to Delilah.

Winner: Once Brad and Carter's votes have been transferred Andrea has a majority of votes and so is the winner.

The Supplementary Vote and Sri Lankan contingent vote are two implemented variation in which voters, unlike ordinary form of the contingent vote, cannot rank all of the candidates, but rather are only permitted to express two and three preferences respectively.

This means that if a voter does not use either of his preferences to support one of the candidates who survives to the second round then it will be impossible to transfer his vote, which is therefore 'wasted' or 'exhausted'.

Under the supplementary vote (SV), voters express a first and second choice of candidate only, and, if no candidate receives an absolute majority of first-choice votes, all but the two leading candidates are eliminated and the votes of those eliminated redistributed according to their second-choice votes to determine the winner. The supplementary vote is used in all elections for directly elected mayors in England, including the Mayor of London, and in elections for Police and Crime Commissioners.

In the early 1990s, the Plant Commission was established by the Labour Party, which was then in opposition, to recommend a new voting system for the Parliament of the United Kingdom. When the Commission reported in 1993, instead of suggesting an already existing system, it recommended the Supplementary Vote (SV) system, which had never been used anywhere. Although some commentators credit the invention of SV to Plant, it was actually the brainchild of the then Labour Member of Parliament (MP) for Workington, Dale Campbell-Savours, who advocated and outlined it in an article he wrote for an issue of the left-leaning New Statesman magazine that was published four years before Plant reported, on September 29, 1989.

However, it never became official Labour Party policy to introduce SV for national elections in the United Kingdom. Prior to 2000, there were no directly elected mayors in England but, when direct elections were introduced for some mayors, it was decided to use SV and it is now in use for the direct election of eleven English mayors, including the Mayor of London.

Each voter ranks at least one and no more than two candidates by placing an 'X' in one column to indicate his or her first choice of candidate and another 'X' in a second column to indicate his or her second choice of candidate. In the first round of counting only first preferences are tallied. If any candidate has an absolute majority of votes (i.e. more than half) at this stage then they are declared elected. If no candidate has a majority then all candidates except the two with most first preferences are eliminated and the count proceeds to a second round. In the second round any voter whose first preference has been eliminated has his vote transferred to the candidate of his second preference (but only if his second choice has not also been eliminated). The candidate with the most votes is then declared elected.

A less common form is to print a single column on the ballot paper and require voters to write '1' next to their first preference and '2' next to their second. This form was used to elect the Mayor of Newham in the 2006 election.

The Supplementary Vote is said to encourage candidates to seek support beyond their core base of supporters in order to secure the second preferences of the supporters of other candidates and so to create a more conciliatory campaigning style among candidates with similar policy platforms. SV is also likely to improve the chances of 'third party' candidates by encouraging voters who wish to do so to vote sincerely for such candidates where under systems such as 'first past the post' they would be discouraged from doing so for tactical reasons.

These potentially positive effects will be moderated, however, by the strong incentives SV creates for voting, in most circumstances, for only candidates from among the leading three. The Electoral Reform Society criticised SV following the mayoral election in Torbay in October 2005, claiming that 43.5% of second preference votes were ignored as not being given to either of the top two placed candidates, disadvantaging supporters of non-party candidates[1].

First, since the automatic dual-ballot nature of SV dispenses with any need for a runoff two weeks later - as often happens for, say, the election of the president of France - voters go in casting their second preferences with little or no idea of which candidates will make the runoff. Consequently, many second preferences will be declared invalid because they have been cast for eliminated candidates. It could be said here, of course, that a cursory look at opinion polls taken during the campaign would give voters an informed idea of which candidates are the front-runners; however not all elections using the system have opinion polls conducted and published.

Second, it is possible for the victor to fail to achieve an absolute majority overall, i.e. by total first and second preference votes, since it is not an obligation for a voter to cast a second preference and, moreover, a second preference will be ineffective unless it is cast for a candidate who makes it into the top two. They argue that this is important as victors may still claim, in such cases, to have won a clear majority mandate from the voters when, in fact, they have not. They remark further: 'It is perhaps surprising that the [British] government did not opt for AV [the Alternative Vote], which requires only a single ballot and guarantees a majority winner'.[1]

Like other forms of the Contingent Vote, the Supplementary Vote is not a form of proportional representation and so, were it used to elect a council or legislature, it could be expected to produce results similar to other systems involving single seat constituencies such as the 'first past the post' (plurality) system.

In Sri Lanka a variant of the contingent vote electoral system is used to elect the President. As under the conventional contingent vote, in an election held using the Sri Lankan form of the contingent vote each voter ranks the candidates in order of preference, and if no candidate receives an overall majority of first preference votes on the first count then all but the two leading candidates are eliminated and their votes redistributed to help determine a winner in a second and final round. However, whereas under the ordinary form of the contingent vote voters can rank all of the candidates in order of preference, under Sri Lankan CV the voter only expresses his or her top three preferences. Sri Lankan CV has been used for presidential elections there since 1982.

Under the two-round system (also known as 'runoff voting' and the 'second ballot') voters vote for only a single candidate, rather than ranking candidates in order of preference. As under the contingent vote, if no candidate has an absolute majority in the first round, all but the top two are eliminated and there is a second round. However, in the two round system, voters are asked to return and vote a second time. Because of the similarities between them, the contingent vote and the two-round system can usually be expected to elect the same winner. However, in the two-round system, the voter is permitted to change one's mind from one round to another, even if the favourite candidate in the first round has not been eliminated.

As noted above, the alternative vote differs from the contingent vote in that it permits several rounds rather than just two. Under the alternative vote only candidate(s) for whom it is mathematically impossible to win are eliminated after each round, and as many rounds occur as are necessary to give one candidate an absolute majority. These differences mean that the contingent vote and alternative vote can produce different results. Because, under the contingent vote, all but two candidates are eliminated in the first round, it is possible for a candidate to be eliminated who would have gone on to win had he been allowed to receive transfers in later rounds.

If the election in Example II had been conducted using IRV instead of the contingent vote then the winner would have been Carter rather than Andrea. This is because the election would have proceeded as follows:

Andrea

Brad

Carter

Delilah

Round 1

28%

14%

27%

31%

Round 2

28%

14% 0

41%

31%

Round 3

28% 0

69%

31%

Round 1: First preferences are tallied and no candidate has a majority.

Round 2: Under IRV only one candidate is now eliminated. This is Brad, as he has the fewest votes. His votes all transfer to Carter.

Round 3: There is still no candidate with an absolute majority. Now Andrea has the fewest votes so she is eliminated. Her votes all transfer to Carter, who then has an absolute majority.

Winner: After three rounds, Carter is elected.

Note: Arrow's impossibility theorem demonstrates that no voting system based on ranked preferences can possibly meet a certain set of reasonable criteria when there are three or more candidates to choose from. In the above example, it is as possible that Andrea could be a stronger majority compromise candidate, able to win an absolute majority against Carter head-to-head and also beat and Delilah head-to-head, which IRV can not recognize by its sequential elimination. Contingent vote treats the top two candidates equally, and like plurality, it can predictably reward the strongest candidates, those who are selected as first choice among the most voters.

Like virtually all electoral systems (see the Gibbard-Satterthwaite theorem), the contingent vote is open to tactical voting. In particular, like both the two round system and instant-runoff voting, it is vulnerable to the tactics of 'push-over'[citation needed] and 'compromise'. Under the contingent vote compromising occurs where a voter gives a first or other high preference to a candidate not because they necessarily support them, but as a way of avoiding the election of a candidate who they dislike even more. The contingent vote is more vulnerable to compromising than IRV. In the first example given in this article if a large number of Catherine supporters had 'compromised', and given a first preference to Brian, then Brian would have been elected instead of Andrew, a candidate who Catherine supporters dislike even more. This tactic would have been effective under IRV as well as the contingent vote. In Example II Brad supporters, had they predicted that Brad would not make it to the second round, could have compromised by giving their first preferences to Carter, and thereby have ensured his election. This would not have been a necessary tactic under IRV because the votes of Brad supporters would have ended up with Carter anyway—when Brad was eliminated they would have transferred to him.

However the contingent vote is less vulnerable to the tactic of compromise than the 'first-past-the-post' (plurality) system. This is because the contingent vote's system of transferring votes means that even if a voter's first choice is unlikely to be elected, her vote may still have a chance to be transferred to one of her subsequent preferences. In Example I above Catherine would have won under the plurality system because she has more votes than any other candidate. However Brian voters would have been able to ensure the election of their second choice, Andrew, by voting tactically for Andrew instead of Brian, but this contingent (tactical) vote would prevent Brian's electoral support being recorded, thus in a plurality or First-past-the-post voting system 3rd party candidates are either labelled Spoilers or their real support goes unrecognised. Contingent voting is not necessary under IRV because (in this example) Brian's votes will transfer to Andrew in the second round anyway.

'Push-over' is a tactic by which a voter insincerely ranks an unpopular 'push-over' candidate higher than her real first choice. The purpose of voting for the 'push-over' is to ensure that it is this weak candidate, rather than a more popular rival, who remains to challenge her preferred candidate in the second round. By supporting a push-over candidate it is hoped to eliminate a stronger candidate who might have gone on to win the election. Under the contingent vote a voter uses the tactic by giving her first preference to a 'push over' and her lower preferences to the candidates she really supports.

The push-over tactic requires voters to be able to reliably predict how others will vote. It runs the risk of backfiring, because if the tactical voter miscalculates then the candidate intended as a push-over might end up actually beating the voter's preferred candidate. It also requires voters to understand the tactic and be aware that it exists. For these reasons some doubt that push-over is likely to be a factor in real elections. Because under the contingent vote, as under IRV, it is paradoxically possible to harm the chances of a candidate by giving them a first preference, or to aid the chances of a candidate by ranking them lower than first, the system is said to fail the monotonicity criterion.

The contingent vote can be influenced by the same forms of strategic nomination as IRV and the two round system.[citation needed] Strategic nomination is where candidates and political factions influence the result of an election by either nominating extra candidates or withdrawing a candidate who would otherwise have stood. The contingent vote is vulnerable to strategic nomination for the same reasons that it is open to the voting tactic of 'compromising'. This is because it is sometimes necessary for a candidate who knows they are unlikely to win to ensure that another candidate he supports makes it to the second round by withdrawing from the race before the first round occurs, or by never choosing to stand in the first place. By withdrawing candidates a political faction can avoid the 'spoiler effect', whereby a candidate 'splits the vote' of her supporters and prevents any candidate acceptable to them from surviving to the last round. For instance, in Example I above, if Catherine had chosen not to stand then Brian would have been elected instead of Andrew, a more desirable result for Catherine's supporters. However the contingent vote's system of transfers makes it less vulnerable to the spoiler effect than the plurality system.

Like IRV and the two round system, the contingent vote is said to encourage candidates to seek support beyond their core base of supporters in order to secure the lower preferences of the supporters of other candidates. This is said to create a more conciliatory campaigning style among candidates with similar policy platforms. However this effect will be diminished by the fact that lower preferences are less important under the contingent vote than under IRV; under the contingent vote it is especially important for candidates to receive many first preferences so that they are not eliminated straight away.

The contingent vote is not a form of proportional representation, and therefore, if used to elect a council or legislature, it overrepresents larger parties at the expense of smaller ones, and encourages a two party system, in the same manner as other systems based on single seat constituencies (districts), such as 'first past the post', instant run-off and the two round system. However the contingent vote does aid the chances of 'third party' candidates to some extent, by encouraging voters who wish to do so to vote sincerely for such candidates where under 'first past the post' they would be discouraged from doing so for tactical reasons.